= Brownian zero mode of a fluctuating interface
{c}
{title2=$dh_0=\sigma\,dW_t$}
An unpinned uniform height driven by <Gaussian white noise> is <Brownian motion>. Its <variance> grows as $\sigma^2t$ and it has no <stationary distribution> on the real height axis for $\sigma>0$. Indeed, a stationary <characteristic function> would obey $\widehat\mu(k)=\widehat\mu(k)e^{-\sigma^2k^2t/2}$, incompatible with continuity at zero. Quotienting out the uniform height can still leave stationary shape fluctuations.
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